Logic and Foundations Commons^™

New Challenges In Neutrosophic Theory And Applications, Florentin Smarandache, Stefan Vladutescu, Miihaela Colhon, Wadei Al-Omeri, Saeid Jafari, Muhammad Zahir Khan, Muhammad Farid Khan, Muhammad Aslam, Abdur Razzaque Mughal

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic theory has representatives on all continents and, therefore, it can be said to be a universal theory. On the other hand, according to the three volumes of “The Encyclopedia of Neutrosophic Researchers” (2016, 2018, 2019), plus numerous others not yet included in Encyclopedia book series, about 1200 researchers from 73 countries have applied both the neutrosophic theory and method. Neutrosophic theory was founded by Professor Florentin Smarandache in 1998; it constitutes further generalization of fuzzy and intuitionistic fuzzy theories. The key distinction between the neutrosophic set/logic and other types of sets/logics lies in the introduction of the degree of …

(Φ, Ψ)-Weak Contractions In Neutrosophic Cone Metric Spaces Via Fixed Point Theorems, Florentin Smarandache, Wadei F. Al-Omeri

Branch Mathematics and Statistics Faculty and Staff Publications

In this manuscript, we obtain common fixed point theorems in the neutrosophic cone metric space. Also, notion of (Φ, Ψ)-weak contraction is defined in the neutrosophic cone metric space by using the idea of altering distance function. Finally, we review many examples of cone metric spaces to verify some properties.

There Is No Constant In Physics: A Neutrosophic Explanation, Victor Christianto, Robert Neil Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T,I,F (truth, indeterminacy, falsehood) which can take a range of values. Similarly, in this paper we consider NL applications in physics constants. Those constants actually all have a window of plus and minus values, relative to the average value of the constant. For example, speed of light, c, can vary in a window up to +/- 3000 m/s. Therefore it should be written: 300000 km/s +/- 3 km/s. We also discuss some implications of this new …

Octagonal Neutrosophic Number: Its Different Representations, Properties, Graphs And De-Neutrosophication With The Application Of Personnel Selection, Muhammad Saqlain, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

To deal with fluctations in decision-making, fuzzy / neutrosophic numbers are used. The problem having more fluctuations are difficult to sovle. Thus it is a dire need to define higher order number, also It is a very curious question by researchers all around the world that how octagonal neutrosophic number can be represented and how to be graphed? In this research article, the primarily focused on the representation and graphs of octagonal neutrosophic number. at last, a case study is done using VIKOR method based on octagonal neutrosophic number. These representations will be helpful in multi-criteria decision making problems in …

N-Refined Neutrosophic Vector Spaces, Florentin Smarandache, Mohammad Abobala

Branch Mathematics and Statistics Faculty and Staff Publications

This paper introduces the concept of n-refined neutrosophic vector spaces as a generalization of neutrosophic vector spaces, and it studies elementary properties of them. Also, this work discusses some corresponding concepts such as weak/strong n-refined neutrosophic vector spaces, and n-refined neutrosophic homomorphisms.

Extension Of Hypergraph To N-Superhypergraph And To Plithogenic N-Superhypergraph, And Extension Of Hyperalgebra To N-Ary (Classical-/Neutro-/Anti-)Hyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We recall and improve our 2019 concepts of n-Power Set of a Set, n-SuperHyperGraph, Plithogenic n-SuperHyperGraph, and n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra respectively, and we present several properties and examples connected with the real world.

Three Possible Applications Of Neutrosophic Logic In Fundamental And Applied Sciences, Victor Christianto, Robert Neil Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In Neutrosophic Logic, a basic assertion is that there are variations of about everything that we can measure; the variations surround three parameters called T,I,F (truth, indeterminacy, falsehood) which can take a range of values. This paper shortly reviews the links among aether and matter creation from the perspective of Neutrosophic Logic. Once we accept the existence of aether as physical medium, then we can start to ask on what causes matter ejection, as observed in various findings related to quasars etc. One particular cosmology model known as VMH (variable mass hypothesis) has been suggested by notable astrophysicists like Halton …

New Notions From (R; S)-Generalized Fuzzy E-Open Sets, A. Vadivel, P. Periyasamy, V. Chandrasekar, G. Saravanakumar

Applications and Applied Mathematics: An International Journal (AAM)

The present article discuss (r; s)-generalized fuzzy e-border, (r; s)-generalized fuzzy e-exterior and (r; s)-generalized fuzzy e-frontier in double fuzzy topologies. Furthermore, some characterizations of generalized double fuzzy e-continuous, generalized double fuzzy e-open, generalized double fuzzy e-closed and generalized double fuzzy e-closure-irresolute functions are studied and investigated. Moreover, the interrelations among the new concepts are discussed with some necessary examples.

Fuzzy Semi-S-Irresolute Continuous Mappings In Šostak’S Fuzzy Topological Spaces, B. Vijayalakshmi, J. Praba, M. Saraswathi, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the concepts of fuzzy semi-S-irresolute open map, fuzzy semi-S-irresolute closed map and fuzzy semi-S-irresolute homeomorphism to the fuzzy topological spaces in Šostak’s sense are introduced and studied. Some of their characteristic properties are considered. Also a comparison between these new types of functions are established by giving examples.

Modest Automorphisms Of Presburger Arithmetic, Simon Heller

Dissertations, Theses, and Capstone Projects

It is interesting to consider whether a structure can be expanded by an automorphism so that one obtains a nice description of the expanded structure's first-order properties. In this dissertation, we study some such expansions of models of Presburger arithmetic. Building on some of the work of Harnik (1986) and Llewellyn-Jones (2001), in Chapter 2 we use a back-and-forth construction to obtain two automorphisms of sufficiently saturated models of Presburger arithmetic. These constructions are done first in the quotient of the Presburger structure by the integers (which is a divisible ordered abelian group with some added structure), and then lifted …

A Hybrid Plithogenic Decision-Making Approach With Quality Function Deployment For Selecting Supply Chain Sustainability Metrics, Florentin Smarandache, Mohamed Abdel-Basset, Rehab Mohamed, Abd El-Nasser H. Zaied

Branch Mathematics and Statistics Faculty and Staff Publications

Supply chain sustainability has become one of the most attractive decision management topics. There are many articles that have focused on this field presenting many different points of view. This research is centred on the evaluation of supply chain sustainability based on two critical dimensions. The first is the importance of evaluation metrics based on economic, environmental and social aspects, and the second is the degree of difficulty of information gathering. This paper aims to increase the accuracy of the evaluation. The proposed method is a combination of quality function deployment (QFD) with plithogenic aggregation operations. The aggregation operation is …

Cubic Interior Ideals In Semigroups, G. Muhiuddin

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we apply the cubic set theory to interior ideals of a semigroup. The notion of cubic interior ideals is introduced, and related properties are investigated. Characterizations of (cubic) interior ideals are established, and conditions for a semigroup to be left (right) simple are provided.

Category Theory And Universal Property, Niuniu Zhang

Honors Theses

Category theory unifies and formalizes the mathematical structure and concepts in a way that various areas of interest can be connected. For example, many have learned about the sets and its functions, the vector spaces and its linear transformation, and the group theories and its group homomorphism. Not to mention the similarity of structure in topological spaces, as the continuous function is its mapping. In sum, category theory represents the abstractions of other mathematical concepts. Hence, one could use category theory as a new language to define and simplify the existing mathematical concepts as the universal properties. The goal of …

Computable Reducibility Of Equivalence Relations, Marcello Gianni Krakoff

Boise State University Theses and Dissertations

Computable reducibility of equivalence relations is a tool to compare the complexity of equivalence relations on natural numbers. Its use is important to those doing Borel equivalence relation theory, computability theory, and computable structure theory. In this thesis, we compare many naturally occurring equivalence relations with respect to computable reducibility. We will then define a jump operator on equivalence relations and study proprieties of this operation and its iteration. We will then apply this new jump operation by studying its effect on the isomorphism relations of well-founded computable trees.

Formally Verifying Peano Arithmetic, Morgan Sinclaire

Boise State University Theses and Dissertations

This work is concerned with implementing Gentzen’s consistency proof in the Coq theorem prover.

In Chapter 1, we summarize the basic philosophical, historical, and mathematical background behind this theorem. This includes the philosophical motivation for attempting to prove the consistency of Peano arithmetic, which traces itself from the first attempted axiomatizations of mathematics to the maturation of Hilbert’s program. We introduce many of the basic concepts in mathematical logic along the way: first-order logic (FOL), Peano arithmetic (PA), primitive recursive arithmetic (PRA), Gödel's 2nd Incompleteness theorem, and the ordinals below ε₀.

In …

Extension Of Soft Set To Hypersoft Set, And Then To Plithogenic Hypersoft Set, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the soft set tothe hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

Experience Of A Noyce-Student Learning Assistant In An Inquiry-Based Learning Class, Melissa Riley

UNO Student Research and Creative Activity Fair

This presentation refers to an undergraduate course called introduction to abstract mathematics at the University of Nebraska at Omaha. During the academic year 2017-2018, undergraduate, mathematics student Melissa Riley was a Noyce-student learning assistant for the Inquiry Based Learning (IBL) section of the course. She assisted the faculty-in-charge with all aspects of the course. These included: materials preparation, class organization, teamwork, class leading, presentations, and tutoring. This presentation shall address some examples of how the IBL approach can be used in this type of class including: the structure of the course, the activities and tasks performed by the students, learning …

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_V on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and …

A Short Remark On Gödel Incompleteness Theorem And Its Self-Referential Paradox From Neutrosophic Logic Perspective, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

It is known from history of mathematics, that Gödel submitted his two incompleteness theorems, which can be considered as one of hallmarks of modern mathematics in 20th century. Here we argue that Gödel incompleteness theorem and its self-referential paradox have not only put Hilbert’s axiomatic program into question, but he also opened up the problem deep inside the then popular Aristotelian Logic. Although there were some attempts to go beyond Aristotelian binary logic, including by Lukasiewicz’s three-valued logic, here we argue that the problem of self-referential paradox can be seen as reconcilable and solvable from Neutrosophic Logic perspective. Motivation of …

Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. Ii, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.